A. Field of the Invention
The present invention relates generally to devices and methods for measuring the freezing points of liquids. The present invention relates more specifically to an apparatus and a method for measuring the freezing point of liquids by employing a very small sample of a liquid and by numerically analyzing the thermal characteristics of the liquid.
B. Description of Related Art
Whenever a substance is utilized in an environment that potentially allows for the substance to change phase, an accurate knowledge of this phase change would be desirable in order to control the effects this phase change might have on the performance of the substance. Systems that are designed to handle liquids, for example, frequently experience difficulties when the liquids change over to the gaseous state and yet continue to be contained and handled by mechanisms designed for liquids. Similarly, when a system is designed to handle liquids and the possibility exists that these liquids could solidify, a concern for the point at which solidification begins to occur and the effects that solidification has on the system becomes important. An example of this concern can be seen in the aircraft industry where the presence of low temperatures at high altitudes increases the potential for the freezing of hydrocarbon based fuels and lubricants.
The present invention is concerned with determining the point at which a substance changes phase between a liquid and a solid. Strictly speaking, the freezing point of a substance is defined as the temperature at which both liquid and solid may exist in equilibrium. In the real world, the concern for the freezing point of a substance begins when crystalline solids start to form, or finally disappear as the case may be, from the liquid phase of the substance. The "freezing point", therefore, that is of concern here is that point at which all solids have been transformed into liquids, when looking at a transition from the solid to the liquid phase, or the point at which solids begin to form, when looking at the transition from the liquid to the solid phase.
There are many methods for determining the point at which this liquid-solid phase change occurs. A number of physical properties of the substance can be measured which reflect the presence or absence of crystalline solids in combination with the liquid substance. The present invention is primarily concerned with a specific thermal technique for determining the presence or absence of these solids. An analysis of the way in which heat is absorbed or removed from the substance and the resultant temperature changes in the substance can provide an indication of the point at which crystals start to form, or finally disappear, in the liquid.
The change between a liquid and a solid can, of course, move in two directions. A liquid may solidify and a solid may liquify, both phase changes passing through the freezing point of concern here.
An analysis of these phase changes for the purposes of this invention directly involves measurements of time and temperature and indirectly involves an analysis of the heat flow in and out of the substance.
For a substance composed of a single compound, the heat flow and the changes in temperature with respect to time can be described and analyzed very simply. As such a substance is cooled while in the liquid state, heat is removed from the substance and flows into the surrounding environment. This heat flow out of the substance is reflected by a corresponding temperature decrease in the liquid.
The heat flow out of the substance during this cooling process is essentially the exchange of energy between the substance and the surrounding environment. In the first instance, over a temperature range above the freezing point of the substance, the energy flow out of the liquid reflects a decrease in the kinetic energy of the molecules in the liquid. This decrease in kinetic energy is measured as a decrease in the temperature of the liquid. At the freezing point of the substance, the energy exchange from the substance to the environment does not derive from a change in the kinetic energy of the molecules, but rather derives from the reorganization of the molecules in the substance into the crystalline lattice of a solid. The crystalline lattice structure of a solid allows the molecules to exist at a lower energy state. There is a net difference in energy between molecules existing in a liquid state at a given temperature and molecules existing in a solid state at that same temperature. As a "cooling" of the substance continues, more and more molecules are arranged in the crystalline lattice structure and release a corresponding amount of energy into the environment that is exhibited as a continued heat flow ("latent heat") out of the substance. Once all such liquid molecules have arranged themselves in the solid structure and have released a corresponding amount of energy as a result, then the continued cooling of the substance reverts back to a continued decrease in the kinetic energy of the molecules. This is reflected by a continued decrease in the temperature of the now solid substance.
The problem with examining and analyzing the phase change on the cooling curve described above is the phenomenon known as "supercooling" that occurs in a liquid prior to its phase change into the solid state. Supercooling occurs when the temperature continues to drop below the freezing point of the substance without any crystalline structures forming. Whether and to what extent a substance tends to supercool rather than undergo a phase change at its freezing point is often a function of the purity of the substance and the presence or absence of seed crystals or seed surfaces within the liquid.
The warming curve of a substance on the other hand is more appropriately and more accurately a source of determining the actual freezing point of the substance. In much the reverse of the cooling curve, a warming curve describes an energy or heat flow into the solid substance which corresponds to an increase in the temperature of the solid indicative of an increase in the kinetic energy of the molecules in the solid. At a certain point, the kinetic energy of the molecules is sufficient to break the crystalline lattice structure of the solid and allow the molecules to move freely in a liquid state. Once the energy flow into the substance initiates this phase change from the solid to the liquid state, the energy into the substance is no longer reflected by an increase in the temperature, but is reflected instead by the continued movement of molecules from the solid state to the liquid state. When the energy or heat input into the substance is sufficient to completely change all molecules from the solid state to the liquid state, then the continued flow of energy into the substance is again reflected by an increase in the temperature of the substance. The point at which this change occurs, the so called "knee of the curve", is the point at which the last molecules absorb energy from the environment and break themselves free from the crystalline lattice structure to exist in the liquid phase. It is this point at which the temperature of the substance begins to rise again in response to the continued flow of energy, that can readily be measured so as to determine the "melting point" of the substance, and in fact, does represent a characteristic point at which the crystalline form of the material no longer exists.
For a substance that is not a single compound, but rather is a mixture of various compounds, each with separate freezing points, an analysis of the critical temperature becomes more complicated. Rather than a sharp transition from a heat flow that results in a temperature change to a heat flow that results in the phase change, there is a gradual change over from one to the other. Therefore, as a mixture passes through the range of freezing points for its various components, some of the heat being exchanged with the environment reflects a temperature change and some of the heat reflects a phase change. It is therefore difficult to determine either the first point at which crystals begin to form in the liquid substance on the cooling curve, or the last point at which crystals exist in the substance on the warming curve. Such determinations require a more careful analysis of the rate of change of temperature rather than simply the identification of the point at which the temperature begins to change again. The "plateau" that clearly exists in the temperature curve of a pure substance, will typically be vague and undefined in the temperature curve of a mixture.
There have been many attempts in the past to provide devices and methods for determining the freezing points of liquid mixtures. Some of these methods focus on measurements associated with the cooling curve. The problems already described above with regard to the cooling curve have not entirely been eliminated, and more accurate and reliable measurements continue to be made with an analysis of the warming curve.
Attempts in the past to measure and analyze the warming curve have focused on determining an "inflection point" during which the rate of temperature change decreases, and then increases over a short time interval. The methods used in the past gather temperature data relative to time, as the substance is warmed, and use differentiators to determine an inflection point of the temperature curve. The first derivative, which is an indication of the rate of change of the temperature, can be determined and used to define the inflection point as a peak or valley in an otherwise smooth curve.
The problem with these methods, apart from the fact that they require electronic differentiators and generally require microprocessors that can handle first derivative analysis of the data, is that their results fail to coincide with the accepted standardized results obtained by methods specified by the American Society For Testing Materials (ASTM) Method Number D2386 and the Institute of Petroleum (IP) Method Number IP-16, which are identical and which are world wide accepted standard test methods. In theory, an accurate first derivative differentiation and perhaps a second derivative differentiation of the warming curve may produce a value closest to the true "freezing point". But the reality is that anyone concerned with the "freezing point" of a liquid in the real world, will want to make a determination of the freezing point that is in accord with the accepted standards. Therefore, while the careful and exacting analysis of many of the existing methods provide an interesting theoretical study, they do not provide the practical method that the real world user of such a device would require.
Apart from the shortcomings of the methods described above, the devices that have been designed to be used in association with these methods have a number of short comings in and of themselves. Basically, all of these devices, whether measurements are made on the cooling curve or on the warming curve, require some method of cooling a sample of liquid and then controllably rewarming the sample through the critical freezing point. For most substances of concern, the freezing point of the liquid is somewhere below room temperature and thus the devices that are used necessarily have cooling components which can reduce the temperature of the liquid sample below that of room temperature.
Cooling systems have never been simple or compact. In order to withdraw heat from a substance, the device must provide a large thermal reservoir that can be placed in contact with the substance and not rapidly become "saturated" with the heat that is drawn from the substance. If such a reservoir is to be a solid substance, as is the case with thermoelectric heat pumps, it must be of sufficient size to allow the rapid dissipation of the heat throughout its structure and not allow that area of its structure that is in contact with the substance to build up with the heat from the substance and thereby slow down the cooling. On the other hand, the use of liquids and gases to provide cooling can likewise involve significantly cumbersome mechanisms. Cooling systems that function with compressors (the typical principal upon which most commercial refrigeration systems function) require large amounts of energy to run, are usually large and heavy, and seldom are capable of rapidly cooling a substance to the low temperatures necessary in many applications.
There is a direct relationship between the size of the sample and the resultant size of cooling apparatus necessary to sufficiently reduce the temperature of the sample below its freezing point. Clearly, the smaller the sample that is required, the less cumbersome the cooling system that is necessary. On the other hand, it is important that the cooling system be sufficiently controllable as to allow for the accurate measurement of the freezing point, as it is passed, in a reasonable period of time. The problems associated with many of the previous attempts to control the warming and cooling of a substance in order to determine its freezing point, have frequently been associated with the bulky devices that are required for this controllable warming and cooling. Furthermore, the size of equipment can possibly preclude its use in today's busy and crowded laboratories where space is already a premium.
It would be advantageous to have a method and device which in combination can provide both procedural simplicity and structural compactness that is desirable, and still achieve an accurate determination of the freezing point that is in accord with accepted standards, all within the confines of more simplified cooling and warming controls. While large, elaborate warming and cooling systems might eliminate most of the undesirable influences of a testing environment and might accurately control warming rates, they have by experience created "overly exact" readings of the freezing point. If a method were found that could accurately measure the freezing point in accordance with acceptable standards and could do so with a device that was sufficiently compact and simple, then the proper balance between practicality and accuracy would be realized.
FIG. 4 in the drawing discloses a graph which describes in general terms the methods by which previous devices have most successfully attempted to determine the freezing point of certain typical petroleum liquid fuels. FIG. 4 is a graph of the relationship between two variables, x representing time on the horizontal axis, and T(x) representing relative temperature on the vertical axis. The primary curve disclosed in the graph is the solid line with intermittent dots. This curve represents a section of the warming curve for a fuel substance (i.e., a hydrocarbon mixture) passing from the solid state to the liquid state. Each dot on the warming curve represents a discrete data sample at a specific time interval. The duration of the specific time interval depends upon the degree of error desired in the determination of the freezing point. A vague plateau can be discerned near the center of the warming curve in FIG. 4. This plateau is indicative of a phase change from the solid to the liquid state, i.e., a portion of the substance is changing from solid to liquid. During the time interval over which the curve flattens out, the heat being input into the substance does not correspond to a temperature change, but rather is primarily the latent heat of melting that goes into converting the substance from the solid to the liquid phase. The heat input into the substance continues to force the phase change until such time as all of the solid components of the substance have changed to liquid. Once the last solids become liquid the continued flow of heat into the substance once again forces a temperature change. The "freezing point" described above is the point at which the heat flow stops effecting a phase change and starts effecting a temperature change. Theoretically this is the same point at which the standardized methods detect when the last crystal melts.
Methods of determining the freezing point from the warming curve of a substance, have focused primarily on the differentiation of the curve in order to accurately determine the rate of change of the temperature of the substance and therefore the point at which the temperature starts changing again after the phase change. Some previous methods, such as that described in U.S. Pat. No. 4,601,587, issued to Mathiprakasan, utilize the first derivative of the warming curve to determine this "freezing point". The first derivative in FIG. 4 is indicated by the solid line labeled dT/dx. This first derivative, generally speaking, is indicative of the rate of change of the temperature with respect to time. This curve peaks at a point where the rate of change of temperature is high. This point is indicated by the letter A in FIG. 4. It is this value that is used to identify the so called "knee of the curve", and thereby to identify the freezing point temperature.
As mentioned in the above discussion, differentiation may in fact provide an accurate "freezing point" for a given substance. In reality however, the results of these methods have been shown to err by as much as two degrees centigrade from the results determined by the accepted standards in the industry. Industry standards obtain results that are closer to what is shown as the second derivative of the warming curve. The second derivative is shown as a dashed line in FIG. 4 and is labeled by d(dT/dx)/dx. The second derivative generally speaking is an indication of the rate of change of the rate of change of the temperature in the warming curve. As an analogy, if the first derivative is considered to be the speed of temperature change, the second derivative is the acceleration with which the temperature is changing. Therefore, though the temperature may be changing at a greater speed at point A, it is accelerating the greatest at point B. It is this peak "acceleration" in the temperature change that more accurately reflects the "freezing point" results of standardized methods.
The problem with utilizing the second derivative in determining the freezing point lies not only in the complexities of the calculations and the kinds of microprocessors necessary to make the determination, but also in the frequency of independent anomalies in the second derivative curve that could be mistaken for the actual freezing point. If these anomalies could be sufficiently reduced and/or eliminated, then it is conceivable that the second derivative could be a practical way of obtaining freezing point results that are in accord with the standardized tests.
The present invention will be shown to disclose an alternative to utilizing the first or second derivative to determine this freezing point. A unique numerical analysis method has been found to achieve much the same accuracy that the second derivative analysis achieves without the complexity and without the possibility for mistaking an anomaly for the freezing point. This method is described in more detail hereinbelow.